What do the following two equations represent? $x+2y = 1$ $-4x-8y = 3$
Explanation: Putting the first equation in $y = mx + b$ form gives: $x+2y = 1$ $2y = -x+1$ $y = -\dfrac{1}{2}x + \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $-4x-8y = 3$ $-8y = 4x+3$ $y = -\dfrac{1}{2}x - \dfrac{3}{8}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.